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    Generalized fractional integral inequalities of Hermite-Hadamard type for harmonically convex functions
    (Springeropen, 2020) Zhao, Dafang; Ali, Muhammad Aamir; Kashuri, Artion; Budak, Hüseyin
    In this paper, we establish inequalities of Hermite-Hadamard type for harmonically convex functions using a generalized fractional integral. The results of our paper are an extension of previously obtained results (Iscan in Hacet. J. Math. Stat. 43(6):935-942, 2014 and Iscan and Wu in Appl. Math. Comput. 238:237-244, 2014). We also discuss some special cases for our main results and obtain new inequalities of Hermite-Hadamard type.
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    Hermite-Hadamard Type Inequalities For (H)Over-Bar-Convex Function Via Fuzzy Interval-Valued Fractional Q-Integral
    (World Scientific Publ Co Pte Ltd, 2024) Cheng, Haiyang; Zhao, Dafang; Sarıkaya, Mehmet Zeki
    Fractional q-calculus is considered to be the fractional analogs of q-calculus. In this paper, the fuzzy interval-valued Riemann-Liouville fractional (RLF) q-integral operator is introduced. Also new fuzzy variants of Hermite-Hadamard (HH) type and HH-Fejer inequalities, involving (h) over bar -convex fuzzy interval-valued functions (FIVFs), are presented by making use of the RLF q-integral. The results not only generalize existing findings in the literature but also lay a solid foundation for research on inequalities concerning FIVFs. Moreover, to verify our theoretical findings, numerical examples and imperative graphical illustrations are provided.
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    Hermite-Hadamard-type Inequalities for h-preinvex Interval-Valued Functions via Fractional Integral
    (Springernature, 2023) Tan, Yun; Zhao, Dafang; Sarıkaya, Mehmet Zeki
    We present a comprehensive study on Hermite-Hadamard-type inequalities for interval-valued functions that are h-preinvex, using the Riemann-Liouville fractional integral. Our research extends and generalizes some existing results found in the literature. In addition, we provide accurate proofs for the main theorems originally derived by Srivastava et al. in their publication titled ''Hermite-Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators'' (Int. J. Comput. Int. Sys. 15(1):8, 2022). Finally, we illustrate our findings through a practical example to demonstrate the validity of our results.
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    Hermite-Hadamard-type inequalities for the interval-valued approximatelyh-convex functions via generalized fractional integrals
    (Springer, 2020) Zhao, Dafang; Ali, Muhammad Aamir; Kashuri, Artion; Budak, Hüseyin; Sarıkaya, Mehmet Zeki
    In this paper, we present a new definition of interval-valued convex functions depending on the given function which is called interval-valued approximatelyh-convex functions. We establish some inequalities of Hermite-Hadamard type for a newly defined class of functions by using generalized fractional integrals. Our new inequalities are the extensions of previously obtained results like (D.F. Zhao et al. in J. Inequal. Appl. 2018(1):302,2018and H. Budak et al. in Proc. Am. Math. Soc.,2019). We also discussed some special cases from our main results.
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    Some Bullen-Type Inequalities For Generalized Fractional Integrals
    (World Scientific Publ Co Pte Ltd, 2023) Zhao, Dafang; Ali, Muhammad Aamir; Budak, Hueseyin; He, Zai-yin
    In this paper, we establish some new Bullen-type inequalities for differentiable convex functions using the generalized fractional integrals. The main advantage of the inequalities and operators used to obtain them is that these inequalities can be turned into some existing inequalities for Riemann integrals and new inequalities for Riemann-Liouville fractional integral inequalities and k-fractional integrals. Finally, we add some applications of special means of real numbers using the newly established inequalities to make these results more interesting.
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    Some Generalizations of Different Types of Quantum Integral Inequalities for Differentiable Convex Functions with Applications
    (Mdpi, 2022) Zhao, Dafang; Ali, Muhammad Aamir; Luangboon, Waewta; Budak, Hüseyin; Nonlaopon, Kamsing
    In this paper, we prove a new quantum integral equality involving a parameter, left and right quantum derivatives. Then, we use the newly established equality and prove some new estimates of quantum Ostrowski, quantum midpoint, quantum trapezoidal and quantum Simpson's type inequalities for q-differentiable convex functions. It is also shown that the newly established inequalities are the refinements of the existing inequalities inside the literature. Finally, some examples and applications are given to illustrate the investigated results.
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    Some parameterized Simpson's type inequalities for differentiable convex functions involving generalized fractional integrals
    (Springer, 2022) You, Xue Xiao; Ali, Muhammad Aamir; Budak, Hüseyin; Kara, Hasan; Zhao, Dafang
    In this paper, we establish some new inequalities of Simpson's type for differentiable convex functions involving some parameters and generalized fractional integrals. The results given in this study are a generalization of results proved in (Du, Li and Yang in Appl. Math. Comput. 293:358-369, 2017).